fast and curious

Saturday Teaser Curio #75: A Problem of Presidential Probability

Happy Presidents' Day! This week's teaser uses the way we most commonly interact with dead presidents: money. If you have the day off, noodle on this.

Mary has 4 modern US coins, one each of the common denominations (penny, nickel, dime, and quarter) and 4 modern US bills ($1, $5, $10, and $20). She picks up one of the coins or bills at random, looks at it, declares "Wow! That's my favorite US president!", and puts it in her pocket. John, hearing all the hubbub, comes by, picks up one of the remaining coins or bills at random, looks at it, and declares "Wow! That's my favorite US president!". What is the probability that Mary and John have the same favorite US president?

Ready for the answer?

The key to solving this teaser is looking up (or knowing) the people on the currency. On the currency mentioned in the puzzle, there are two presidents who appear on twice (Washington, Lincoln), three presidents who appear only once (Jefferson, Jackson, FDR), and one non-president (Hamilton on the $10 bill).

Given these facts of the problem, the probability that Mary and John have the same favorite president is the same as the probability that they both picked Washington or they both picked Lincoln. Since we know that Mary and John both picked presidents, neither of them picked up the $10 (Hamilton).

So the final answer is the probability that Mary picked Washington (25¢ or $1) or Lincoln (1¢ or $5) AND John picked the other denomination of the same president. That's 4/7 x 1/6 = 2/21 or ~9.5%.